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This research addresses fundamental issues in the mesoscopic thermodynamics of asymmetric fluid interfaces, namely, the nature asymmetric interfacial profile and the curvature dependence of the interfacial tension. In some fundamentally and practically important fluid systems exhibiting smooth interfaces, such as near-critical fluids and polymer solutions,  the amplitude of the first curvature correction to the interfacial tension, known as Tolman’s length, may become as large as the thickness of the interface itself. Tolman’s length depends crucially on the degree of asymmetry in the fluid phase coexistence and on the mesoscopic fluctuations of density or concentration. We are performing a theoretical and computational study of these, yet to be explored, effects on the behavior of curved interfaces in soft matter. The approach we have adopted is semi-phenomenological, based on “gradient theory” and scaling ideas in mesoscopic thermodynamics. The research impacts filtration through micro porous media in oil recovery, microfluidics, nanoscale liquid bridges, nucleation phenomena, and all instances where science and technology deal with fluid droplets at submicron and nano scales. In particular, the interfacial properties of highly asymmetric polymer solutions and polymer blends, ionic fluids near the critical points of phase separation, and two-dimensional phase separation on the surface of vesicles and lamellae are some of the principle subjects of our investigations.

The results of the first year

During the first year, we have generalized the theory of “complete scaling” to mesoscopically inhomogeneous fluids, including systems with smooth interfaces. Complete scaling is a theory which maps the thermodynamics of asymmetric fluids i.e. those fluids with asymmetric phase coexistence, onto the well-developed thermodynamics of symmetric models, such as the lattice gas model. Complete scaling was originally formulated to treat critical phenomena in bulk systems. It postulates that the “theoretical” field variables of the symmetric models can be represented as linear combinations of the physical field variables which describe the actual asymmetric fluid. We have introduced another field variable, which controls the density inhomogeneity, into the field mixing. This allows us to successfully map the complicated thermodynamics of the fluctuation-affected asymmetric interfaces onto the relatively simple thermodynamics of the lattice-gas interface. We have calculated the asymmetric interfacial profile near the critical point of vapor-liquid and liquid-liquid separation and applied the results to such highly asymmetric systems as ethane-heptane mixtures near the vapor-liquid critical point and methanol-hexane-water mixtures near the liquid-liquid critical point.  We have also calculated Tolman’s length, the first curvature correction to the surface tension, and have verified and extended the previously proposed phenomenological relation between Tolman’s length, the thickness of the interface and the bulk densities of the coexisting fluid phases. This, in turn, lead to the introduction of a new critical amplitude ratio.  The ratio depends on a newly proposed asymmetry of the bulk correlation length in the two coexisting phases.  We have suggested a light scattering experiment to verify the universality of the ratio and the asymmetry in the correlation length. The research we have conducted is closely linked to educational activities in the areas of complex fluids and soft-matter science at the University of Maryland. An interdisciplinary course annually taught by the PI is titled “Mesoscopic and Nanoscale Thermodynamics”. The PI is currently writing a textbook for this course. Some results obtained in the grant research have been already included in the course and in the draft of the textbook. We have not published any journal articles related to this work during the first year of the research. A Chapter “Thermodynamics of Fluids at Meso and Nano Scale” in the IUPAC book “Applied Thermodynamics of Fluids” has been accepted for publication by the Royal Society of Chemistry in 2010. However, we have reported the study results at research conferences, namely the 15^th International Conference on the Properties of Water and Steam (Berlin, September 2008), the 2008 AIChE Annual Meeting (Philadelphia, November 2008), APS 2008 March Meeting (Pittsburgh, March 2009), and the 17^th Symposium on Thermophysical properties (Boulder, June 2009).  The travel of two students, Heather St. Pierre and Deepa Subramanian, to the conferences was partially supported by the PRF grant. In August 2009, Heather St. Pierre and graduated with Ph.D degree and Deepa Subramanian graduated with MS degree.